course Mth 151 J]żassignment #012
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16:06:42 ANSWERS/COMMENTS FOR QUERY 12
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RESPONSE --> I understand everything, except for little section on universal quantifiers and existential quantifiers. As I did the examples in the reading and the exercises at the end, I don't believe I got a single one correct. I will have to just read over it again until it sinks in. I also haven't watched the videos yet, which I am sure will help.
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16:07:41 Query 3.1.10 Mary is top grossing film. Is this a statement?
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RESPONSE --> Yes, it is a statement. It is not a command, an opinion or a question.
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16:09:18 ** A sentence is a statement if it is true or false. Otherwise it is not a statement. 'There goes a big one' is not a statement because the word 'big' is open to interpretation so is not a statement. 'There are 3.87 * 10^89 particles in the universe at this instant' is a statement: it is either true or it isn't, though we don't know enough to tell which. The gross receipts for a film can be regarded as hard facts--unlike opinions on whether a film is good, or artistic. If 'a top grossing film' is defined as, say, a top-10 film in gross receipts, then we could ascertain whether it is true or false and we would have a the statement. However, 'top grossing' isn't defined here--does it mean one of the top three for the week, top 10 for the year, or what?--and for that reason we can't decide for sure whether it is true or false. So this sentence couldn't be regarded as a statement. **
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RESPONSE --> From what I read from the chapter, I thought it didn't matter if it was true or false in order to be a statement.
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16:09:39 Query 3.1.12 sit up and behave Is this a statement?
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RESPONSE --> This not a statement since it is a command.
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16:09:48 ** This is not a statement. It is a command. You could evaluate the truth of the statement 'you sat up', but not the truth of the command to sit up. **
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RESPONSE --> ok
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16:10:27 Query 3.1.18 Is this a compound statement or not: 'calif or bust'.
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RESPONSE --> It is not a compound. It does have the word ""or,"" however it is not used in a connecting way.
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16:10:59 ** The meaning of the phrase is actually 'we're gonna get to California or we're gonna break down trying', in which context it is a compound statement involving 'or'. **
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RESPONSE --> All right.
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16:11:16 Query 3.1.30 negate 'some people have all the luck
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RESPONSE --> No person has all the luck.
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16:12:33 ** The negation would be 'all people don't have all the luck', which means 'nobody has all the luck'. The negation of 'some do' is indeed 'all do not', which is the same as 'none do'. The negation of 'all do' is 'some do not'. The negation of 'none do' is 'some do'. COMMON ERROR: Not everyone has all the luck, or equivalently some people do not have all the luck. This is not incompatible with the original statement, and the negation must be incompatible. Both would be true if some do have all the luck and some don't. **
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RESPONSE --> ok
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16:13:12 Query 3.1.42 p: she has green eyes q: he is 48. What is the statement (p disjunction q)?
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RESPONSE --> She has green eyes or he is 48 years old.
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16:13:17 ** The statement is 'She has green eyes or he is 48 yrs. old' **
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RESPONSE --> ok
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16:13:48 Query 3.1.48 What is the statement -(p disjunction q)
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RESPONSE --> It is not the case that she has green eyes or he is not 48 years old.
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16:14:58 ** The correct translation is 'It is not the case that she has green eyes or he is 48 yrs. old'. An equivalent statement, using deMorgan's Laws, would be 'she doesn't have green eyes and he is 48 years old' COMMON ERROR: She doesn't have green eyes or he is not 48 years old. This statement negates p V q as ~p V ~q, which is not correct. The negation of p V q is ~p ^ ~q. **
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RESPONSE --> Is what I answered correct? It is a little from your answer.
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16:15:34 Query 3.1.54 Jack plays tuba or Chris collects videos, and it is not the case that both are so
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RESPONSE --> q v p ~(q ^ p)
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16:16:23 ** The statement 'jack plays or Chris collects' is symbolized by (p U q). The statement that it is not the case that both are so is symbolized ~(p ^ q). The entire statement is therefore (p U q) ^ ~(p ^ q).**
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RESPONSE --> I left out the ""and"" between the two statements.
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16:19:15 3.1.60 true or false: there exists an integer that is not a rational number.
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RESPONSE --> # 60 in the book states: not every picture has a frame. And my answer to that is row A and row B. As to the question: False, because all integers can be made into rational numbers.
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16:19:39 ** A rational number is a number that can be written as p / q, with p and q both integers. Examples are 2/3, -5489/732, 6/2, etc.. Other examples could be 5/1, 12/1, -26/1; these of course reduce to just 5, 12, and -26. The point is that any integer can be written in this form, with 1 in the denominator, so any integer is in fact also a rational number. Thus there is no integer that is not a rational number, and the statement is false. **
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RESPONSE --> ok
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16:20:23 Query 3.1.66 true or false: each rat number is a positive number
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RESPONSE --> False - fractions can be negative.
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16:20:33 ** This is false, and to prove it you need only give an example of a rational number that is negative. For example, -39/12 is a rational number (integer / integer) and is negative. **
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RESPONSE --> ok
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16:21:42 Query 3.1.75 difference between 'all students did not pass the test' is the statement ' not all students passed the test'
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RESPONSE --> All students did not pass the test means that no one passed. Not all students passed the test means that at least one student passed or that at least one student did not pass.
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16:22:03 ** The first statement says that 'all students did not pass', meaning every student didn't pass, i.e., nobody passed the test. The second statement says that not everyone passed--at least one student didn't pass. The second statement doesn't address the question of whether anyone passed or not, so it doesn't necessarily say that some students did pass, but it leaves open the possibility that some did. Since the second statement contains possibilities the first does not the statements are not equivalent. **
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RESPONSE --> ok
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